(9)/(4x)-(5)/(6)=(13)/(12x)

Solution for (9)/(4x)-(5)/(6)=(13)/(12x) equation:

(9)/(4x)-(5)/(6)=(13)/(12x)

We move all terms to the left:

(9)/(4x)-(5)/(6)-((13)/(12x))=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9/4x-(+13/12x)-5/6=0

We get rid of parentheses

9/4x-13/12x-5/6=0

We calculate fractions


(-240x^2)/1728x^2+3888x/1728x^2+(-1872x)/1728x^2=0

We multiply all the terms by the denominator


(-240x^2)+3888x+(-1872x)=0

We get rid of parentheses

-240x^2+3888x-1872x=0

We add all the numbers together, and all the variables

-240x^2+2016x=0

a = -240; b = 2016; c = 0;
Δ = b2-4ac
Δ = 20162-4·(-240)·0
Δ = 4064256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4064256}=2016$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2016)-2016}{2*-240}=\frac{-4032}{-480}
=8+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2016)+2016}{2*-240}=\frac{0}{-480}
=0
$